Sparse partial robust M regression

• Sparse partial robust M regression is a dimension reduction and regression algorithm.
• It is robust with respect to both vertical outliers and leverage points.
• Intrinsic variable selection via sparse modeling can increase the model precision.
• An implementation of the method is available in the software environment R.
• We demonstrate the advantages of the method in a simulation study and for real data.

Sparse partial robust M regression is introduced as a new regression method. It is the first dimension reduction and regression algorithm that yields estimates with a partial least squares like interpretability that are sparse and robust with respect to both vertical outliers and leverage points. A simulation study underpins these claims. Real data examples illustrate the validity of the approach.